Why can't they create a branch for you to work exclusively in? Or why can't they allow you to check out your own copy to create a branch for local editing? Assuming you're using GIT, you'll be free simply merge their changes into your branch and eventually merge your branch into the master.
Not giving you access to an existing repo is setting you up for a failure that isn't your fault, but will blow back on your shoulders, IMO.
I say this because, as AN said, it's going to become more-and-more of a chore to attempt to build a Watch App independently of its host application. Think about attempting to build a Today widget without having the app behind it - while Watch OS 2 makes this a
little less relevant, it's the same principal (just like Today widgets, Watch Apps are extensions to apps). I suggest
checking out the Watch apps architecture.
By your plan, it sounds as if you'd essentially need to mock your host app, which may or may not work or take large amounts of time and effort, only to dump that work for the host app that already exists, while hoping the integration is clean enough or implementation hasn't changed. Not to mention, regardless of how hard to attempt at keeping things synchronized, making merges of a unique Xcode Project into an already built & defined Xcode Project will be so incredibly painful.
I can't advise you off this course more. At the very least, you
need a checked-out complete copy of their repo. None of this copy files and mocking app BS.